Affine2d compose

affine2d-compose · version 1.0.0 · Geometry, location & color · free, no key needed

Compose two exact rational 2D affine maps in first-then-second order.

Use when you need to: compose affine transformations exactly · combine two 2D affine maps · multiply affine transform matrices.

Decide before calling

Read the versioned contract and the supported scope below. Reuse affine2d-compose@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use affine2d-compose@1.0.0 for compose affine transformations exactly. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• compose affine transformations exactly
• combine two 2D affine maps
• multiply affine transform matrices
• apply first transform then second
• exact rational affine composition
• merge planar affine transforms

Not supported

• three dimensional affine maps
• floating point approximation

Behavior

• Coordinates use x'=a*x+c*y+tx and y'=b*x+d*y+ty.
• The result is second(first(p)); order is not commuted.
• Rationals are canonical reduced strings.

Input

• first (object, required)
• second (object, required)

Output

• transform (object, required)
• reference (constant "Foley et al., Computer Graphics: Principles and Practice, affine transformations (2nd ed., 1990)", required)

Limits

• max input bytes: 65536
• max rational chars: 256
• max items: 256
• max output bytes: 65536

Example

Request input:

{
  "first": {
    "a": "1",
    "b": "0",
    "c": "0",
    "d": "1",
    "tx": "2",
    "ty": "-3"
  },
  "second": {
    "a": "2",
    "b": "0",
    "c": "0",
    "d": "3",
    "tx": "0",
    "ty": "0"
  }
}

Response:

{
  "result": {
    "transform": {
      "a": "2",
      "b": "0",
      "c": "0",
      "d": "3",
      "tx": "4",
      "ty": "-9"
    },
    "reference": "Foley et al., Computer Graphics: Principles and Practice, affine transformations (2nd ed., 1990)"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "affine2d-compose",
  "version": "1.0.0",
  "input": {
    "first": {
      "a": "1",
      "b": "0",
      "c": "0",
      "d": "1",
      "tx": "2",
      "ty": "-3"
    },
    "second": {
      "a": "2",
      "b": "0",
      "c": "0",
      "d": "3",
      "tx": "0",
      "ty": "0"
    }
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/affine2d-compose/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"first":{"a":"1","b":"0","c":"0","d":"1","tx":"2","ty":"-3"},"second":{"a":"2","b":"0","c":"0","d":"3","tx":"0","ty":"0"}}'

The machine-readable contract is at /v1/tools/affine2d-compose/versions/1.0.0.

CLI

node cli.mjs run affine2d-compose 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Homography compose: Compose two exact 2D homographies and return a canonical projective matrix.
• Affine2d apply: Apply one exact rational 2D affine map to bounded points or free vectors.
• Affine2d invert: Invert a nonsingular exact rational 2D affine map with canonical output.
• Affine2d fixed set: Classify and compute the exact fixed locus of a rational 2D affine map.
• Homography apply: Apply an exact 2D homography to a homogeneous point or line, including points at infinity.
• Homography invert: Invert an exact nonsingular 2D homography and return a canonical projective matrix.